The loss function for this task is based on the fidelity between the output state of the searched circuit and the output generated by the encoding circuit from Section 4.3 of [1]} (also shown in Fig. REF ) when input states taken from the set of Pauli operator eigenstates and the magic state \(\vert T \rangle \)  are used:
\(\mathcal {S}=\lbrace \vert 0 \rangle , \vert 1 \rangle , \vert + \rangle , \vert - \rangle , \vert +i \rangle , \vert -i \rangle , \vert T \rangle \rbrace \) 
